Cobalt-60 (half-life 5.27 years, molar mass ≈59.93 g/mol) starts as a 10.0 g sample. After 15.81 years, how many MOLES of Co-60 remain, chaining the half-life decay through to a final mole count, not just a mass?

15.81 ÷ 5.27 = exactly 3 half-lives, so the remaining mass is 10.0 × (1/2)³ = 10.0 × 0.125 = 1.25 g. Converting to moles: 1.25 g ÷ 59.93 g/mol ≈ 0.02086 mol. Reporting 1.25 g as the final answer stops one step short, since the question specifically asks for a mole count, not a mass. Converting the ORIGINAL 10.0 g sample to moles first and then applying the decay fraction in the wrong order (10.0/59.93 ≈ 0.1669 mol, then forgetting to multiply by the 0.125 remaining fraction at all) reports the wrong, undecayed mole count. Applying the decay fraction to the WRONG substance's molar mass (using, say, cobalt-59's stable-isotope molar mass instead of Co-60's actual 59.93 g/mol) would introduce an unjustified substitution not supported by the given data.